Calculation of the deflection of an arched truss with suspended elements depending on the number of panels

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The aim of the work - to propose a scheme and analytical calculation of a statically definable planar truss with a suspended lower belt. Methods. The formula for the dependence of the deflection of the truss under the action of a uniform load on the lower belt on its size and the number of panels is derived in the computer mathematics system Maple. The forces in the rods are found from the solution of the general system of equilibrium equations of all nodes in symbolic form. The deflection is calculated using the Maxwell - Mohr's formula. Generalization of a number of formulas for deflection obtained by increasing the number of panels sequentially to an arbitrary number is performed by double induction using two independent parameters. In this case, special operators of the Maple system are used, allowing for a sequence of coefficients in the desired formula to create and solve recurrent equations that satisfy the elements of the sequences. Results. The obtained solutions have a polynomial form for the number of panels. Curves of deflection dependence on the number of panels are constructed and analyzed. Asymptotic properties of solutions are found in the case of a fixed span length of the structure and a given total load. The proposed scheme is a statically determinate structure with two independent parameters of regularity allows for the finding of a fairly simple analytical solution. The resulting formula is most effective in calculating systems with a large number of elements, where numerical methods tend to accumulate rounding errors.

About the authors

Mikhail N. Kirsanov

National Research University “Moscow Power Engineering Institute”

Author for correspondence.
14 Krasnokazarmennaya St, Moscow, 111250, Russian Federation

Doctor of Physical and Mathematical Sciences, Professor, Department of Robotics, Mechatronics, Dynamics and Strength of Machines


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